Puree the blackberries. Pour puree into a sieve and strain out the seeds. This will take a while, just keep pushing the mixture around with a spoon and pushing down on the mixture to extract the juice–yields roughly 1 3/4 cup blackberry juice. Add the sugar, salt, and lemon juice, and pour into your ice cream maker. Process according to your ice cream maker’s instructions, until the mixture is relatively firm. Meanwhile, beat the cream to stiff peaks. Fold the whipped cream into the processed blackberry mixture. Spoon into a freezer-proof container and freeze until sherbet is set, preferably overnight.